No, you're thinking of "local" DNS as being the local installation of the DNS Server role on that server I assume?
Exchange will query whatever you have configured as your DNS servers within your NIC settings, IF those point to your DNS Server installation on the local machine (if you have one), then it may query those, but that's a separate step in the lookup. DNS Server
(that serves results) and DNS Client (that does lookups and caches replies, and which is found on ALL windows machines) are two completely different services.
Whatever DNS server your query goes to (eg as determined by the settings on your NIC), the DNS server will return a result providing the relevant MX records. How the DNS server provides that information is a completely separate process, but if it doesn't
already know the answer (eg it's local or cached) then it will then connect to the internet to do the lookup, and then once completed it will return the result to Exchange.